Initialization alone is insufficient to stabilize MCMC pathways when model weights are changing quickly. Using a low learning rate late in training is a key aspect of stabilizing sampling paths [1]}, [2]}. Intuitively, if the EBM optimizer has a sufficiently low learning rate then MCMC trajectories in the persistent image bank can function as approximate trajectories from the current model, since weights change very little as the persistent states are updated. By annealing in tandem with our initialization, we are effectively using midrun trajectories of length \(K_\text{def}\)  initialized from the generator to update the EBM while we are actually using shortrun trajectories of length \(K\)  from the persistent bank. Annealing is a crucial component for stabilizing both midrun and longrun trajectories. Without annealing, sampling paths are not able to maintain realism for large \(K_\text{def}\) .
